AB and CD are 2 chords on the same side. AB = 12 cm , CD = 24cm.Distance between two parallel chords is 4 cm. FIND the radius of the circle ?

Asked by Vikas | 11th Jan, 2018, 09:07: AM

Expert Answer:

 
begin mathsize 16px style AB equals 12 space cm comma space CD equals 24 space cm space and space LM equals 4 space cm
Let space OL equals straight x space cm
Then comma space OM equals left parenthesis straight x plus 4 right parenthesis space cm
Join space OA space and space OC.
Then comma space OA equals OC equals straight r
Since space the space perpendicular space from space the space centre space to space straight a space chord space bisects space the space chord comma
rightwards double arrow AM equals MB equals 6 space cm space and space CL equals LD equals 12 space cm
In space triangles space OAM space and space OCL comma
OA squared equals OM squared plus AM squared space and space OC squared equals OL squared plus CL squared
rightwards double arrow straight r squared equals left parenthesis straight x plus 4 right parenthesis squared plus 6 squared space space and space space straight r squared equals straight x squared plus 12 squared
rightwards double arrow left parenthesis straight x plus 4 right parenthesis squared plus 6 squared equals straight x squared plus 12 squared
rightwards double arrow straight x squared plus 8 straight x plus 16 plus 36 equals straight x squared plus 144
rightwards double arrow 8 straight x equals 92
rightwards double arrow straight x equals 11.5 space cm
rightwards double arrow straight r squared equals 11.5 squared plus 12 squared
rightwards double arrow straight r equals 16 space left parenthesis approx right parenthesis end style

Answered by Rashmi Khot | 11th Jan, 2018, 09:58: AM